Exam 1

  1. Question

    A machine fills milk into 500500ml packages. It is suspected that the machine is not working correctly and that the amount of milk filled differs from the setpoint μ0=500\mu_0 = 500. A sample of 226226 packages filled by the machine are collected. The sample mean y\bar{y} is equal to 517.2517.2 and the sample variance sn12s^2_{n-1} is equal to 262.56262.56.

    Test the hypothesis that the amount filled corresponds on average to the setpoint. What is the value of the t-test statistic?


    1. 9.853-9.853
    2. 30.50530.505
    3. 22.761-22.761
    4. 2.894-2.894
    5. 15.95815.958

    Solution

    The t-test statistic is calculated by: t=yμ0sn12n=517.2500262.56226=15.958. \begin{aligned} t & = & \frac{\bar y - \mu_0}{\sqrt{\frac{s^2_{n-1}}{n}}} = \frac{517.2 - 500}{\sqrt{\frac{262.56}{226}}} = 15.958. \end{aligned} The t-test statistic is thus equal to 15.95815.958.


    1. False
    2. False
    3. False
    4. False
    5. True